University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
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123

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16
Author:

Quintin Ware

H. Algebra 2 - Semester 1 Final Exam Review Name: Unit 1 - Functions Module 1 - Analyzing Functions \ 1 1 - Domain . Range and End Behavior < , ! For 1- 2, give the domain and range for each function in inequality, set, and interval notation . 7— . y ~r y\ i. 2. ! 6 S -(16 ); t — —Tx ' f (0, 3) + — (2 g f . . . .. j ^ ^ Cd _ f__ L. i *• ^ l x ) -H ! “• I t~H,TJ x ‘ LM^-2 * l /l TCt U*(. / i ( i I tCOcCo } -r 7 ~7 4 • I \L . — } Oo \ .L L 4 r/ ^ I 1 -jI j —|— , 4 ! •“ i i “ 0 - MI2 H-h-* .11.4 i - -- --5 l ^ vc' C ' f y /-| -> — hSj * 3 i 3. Describe the end behavior for the graph in problem 1. x - ) &> y 6$ / / / -o> / y -) ^ J 3 ' u r wS z/ ^ L 1.2 - Characteristics of Function Graphs For 4 - 1 2, use the graph to the right to identify the following: a ,q ) 4. Interval (s) where the function values are increasing. o c~ i p ) o - ( coj - s) (- 5, i) — —*^* (-1.3, 0) t " ' t ( 5. Interval (s] where the function .values are decreasing. HrV Co a ) C7 ,ao ) t t ( 4.7, 0) , ’ (- 3, - 2} 6 . Intervals] where the function valuer are positive. 2 / t>C3 if j 7. Intervals where the function values aye negative . (rty' lfiJJULSjOO ) f ~ CO I 9 . The zeros of the function. ; * /f / v \ / * 'w v t (i ! • 8. Local minimum and local maximum values . cm , i ‘ IMM V. # 7 if i < ' t \ f V; #! 7 10. End Behavior ^- yi/ nr 1 V *i6/ 1 ) * r --- : % • .. ' J / / * iwl • /> i. t i' i) f *if ( i V/ i: y -T - ( \ 1 V .*. — 11. The function A( d ) 0 A5 d 4- 180 models the amounts, in dollars, that Terry's company pays him based on the round trip distance d , in miles, that Terry travels to a job site. How much does Terry’s pay increase for every mile of travel? - » % per 12. The graph shows the height h[t ) of a model rocket t seconds after it is launched from the ground at 48 feet per second. 150 140 130 120 110 100 - r — j - - I-- ~ ; - \i -- -- S * 90 80 - 70 " 60 50 40 3 0 - -i : : r .... . i 5 ! l ! . 5 : »» f t imuH »» : Ti ! j i \ ...i ' < «« § i«a« • •» 4 \! Ii i : : \ ' . I i j iaafkft » i i u i i i i f c . increasing? i . 1 4 s \—s—i 2 3 4 E f 13. < • (< • < > > f| ( «« « IS . > i 7 6 » t 3 28 2 21 1 10 Ci ( 4 ) decreasing? : x y SH D What interval of time is the height of the rocket MM 5 i C What interval of time is the height of the rocket : - 20 10 " !' lli 1 : A. What is the maximum height the rocket reaches? t.- I B. At what time does it reach its maximum height? ; 5 . itmul V \ r I !•••• 5 52 4 37 a. Use calculator to make a scatter plot. = b. Make a best fitted line and find the function of the line. U) I6X + - c( ' c. Predict the value of y when x =10 i d. Is your prediction from part c an interpolation or extrapolation? 1.3 - Transformations of Function Graphs 14. Given the general equation g ( x ) = a f graph off(x). 5 -l fc h= ihik a= i 17. (x) ^Hot =7, / (U(Ix - 3)) = / ( — 3x) + 1 ftS-£ 4r f ooe / Ho / 1 f*$ L ' Write a function to match each graph shown. 19. 2 “ * i tf±t 8 0 =Z > I n fit, it e t r 1.4 - Inverses of Functions 21. What is the relationship between the points on the graph of function and the points on the graph of \ /\ its inverse? l *1 For 22-23, find the inverse for each function. Write equations in slope- intercept form. 22. f ( x ) A = -4x + 1 2 - - Vy / 1n .X- • / - .. t IVr -U /7 f 6 i . -j- f ?u i - y ./- V . b PXX) W f ..- 4 : _ ‘ I < r? 0 =\o x - 6 23 / (x) • = ISY -C KiC v ? y fv / , h u ( X’ 49 *3 • A> y’ / c7 A/ - 4 . - t: .4- — — 24. Given that the function f ( x]) is defined by the set of point {(0, 1), ( 2, 5), ( 4, 5), and (8, 3)}, what i set of points defines / 1(x)? } V. < O ;\ H? ixo i \v -- • f vv tr -•" > Module 2 - Absolute Value Functions, Equations, and Inequalities ! ' 2.1- Graphing Absolute Values Functions 1. Graph the function f ( x ) = — ^ \x — y ; l| + 3 4 t r4 + 2 - 0. + H 2 I I Njf 4 , P4 / 2 A•> 3 2. Write a function for the graph shown. i xr r" c v - 2.2 Solving Absolute Value Equations - For 3 4, solve each absolute value equation algebraically. Then graph the solution(s) on the number line. 3. \ 2 x — ? 3| = 1 2/ 'LJ < " 1 4.|x ) + 4| + 3 = 2 <7 1 * S Ii VJ Uf i] s / - 6 7 / J \ / i V I / i> c Unit 2 - Quadratic Functions, Relations, and Equations Module 3 - Quadratic Equations 3.1 Solving Quadratic Equations bv Taking Square Roots For 1-3, solve by taking square roots. Tell whether each solution is real or imaginary. Give exact answers. Express imperfect roots in simplified radical form. 1. 2 xz - 16 = 0 ^ 1^% ir 2 2. -5x 2 4- 9 = 0 3. 4x 2 = x 2 - 42 iC *f For problems 4-5, recall the equation for falling objects: 4. A carpenter dropped a hammer from a rooftop 32 feet above ground. How long did it take the hammer to hit the ground? Height (in feet) at time t (in seconds) h( t ) = h0 — 1612 where h0 is the object’s initial height (in feet) : 4 5. An acorn fell from a branch 45 feet high and landed on a branch 8 feet high. How long did it take the acorn to reach the branch ? % ^ - 37 = -/^ tz Solve each quadratic equation by factoring. 6. x 2 7. x 2 ~ 3 x = 18 + 7 x + 12 =\ 0 (v Yf* t) ft -1 11' 1 !. ^ X *4 Vt \ n A : Z' - F> * t • &< ) (YB ) sO K ~UI < f (, 8. x 2 - 64 = 0 - l T V r ( \ XH 3.2 Complex Numbers r . 9. What is the value of imaginary unit, /? - For 10 13, simplify each radical. = — 11.7-27 10.7 49 *07\ | N 5 7* 7' /r - For 14 15, add or subtract the complex numbers. - 14. ( 7 + 2 i) + (5 - -- 1 V ) d - W »i » - lli) c( C l& - fit 2 9 S ' -f £ 4 b( / S’ ^ 2.7 4? 4 ( 19. ( 2 + 0 *7 16. (4 + 90 (6 - 20 tf ' i Z: i " ^ ^ (3 W ~ v! fU £- * p « \ 15. (18 + 27Q - (2 + 3Q For 16 20, simplify. Remember: i 2 — 13.7— 144 12. V 75 = — i '7 v V i- t 1 17. (12i — ^* - 18. (I75 + 3) (i75 3) (7 + 4Q - t j - rt : fi\ + 7 ) *>. 11 f / V ".» 7 ; ? " -VS -?/ \ . ~£~ y . - 3) C*? >7 * 20. (6 + iV 2)(6 - ( V2) ill C 2f > . 3.3 Finding Complex Solutions to Quadratic Equations - For 21 22, complete each square, then write the expression as a binomial squared. n A* yr 21. x 2 + 4x + 5 22. x 2 - lOx + ic 7 L 5 X .. / / For 23- 24, solve by completing the square. State whether the solutions are real or non-real. 23. x 2 — 2x + 7 = 0 M T H -1 - %U HU w • 24. 2 x 2 + 3 x + 4 = 0 ' X —— ± — Vh 2 4ac b 2a ** - 1, P . / it . t T £ /• O' .. --* tit r zy 0 ft* *\ i KrV { ,- V 7 " r /7 >- - f - " Y. } w V f v" l> { -? ± Jvwv A > / ’ • • For 25 - 26, solve each equation using the quadratic formula . i< ' / ^f A 4 2 6. 7 x 2 + 2 x + 3 = — 1 25 . - 5x 2 - 2x - 8 = 0 vr V . . -V Zx -' V^O / V Q — n ^: % 31 r U» s . s: ,: V / ' ‘> t • V < /* -Y V •ft • ^ "' / t ftpa* ' !£ 1 ' — -. (' '.• . t.; £ - - . / (?:' <$ / t ”1 * •V :> i -4 ! i - liTiffi i.. .. *7 *r -:.y > > «/ r % ' IV r -i — i HfW ** .- t i /V . V Vf y ^ \ i 7C J For 27 - 29, use the discriminant to determm&Jhe number and type of solutions to the equation. ( 2 real ” / . L «, Lfet ( 1 real, or 2 non-real] S ‘T 2 2 2-3 18 x 29 x 2 12 3 x . 28 . x + 4 = — 27 . x x= - 8 = x4 4T - O ^}%{ ? > 13 C ) ) VHO f t LAv^ i irc&J - < rv $10 ) 4 W ** < * * * . =• j£& • v“ v' 1 •' • ri ITI'J I'" \ ' *' /o ‘f !* • ; < ( . V . ' ii ' [ 0 • • i• '. ’ ••• •' • 1 ' . j I -- * ? t . ' t. _ ' " - Vv . i .• ? ' . 30.7V Ball is thrown in the air with an initial vertical velocity of 14 m /s from an initial height of 2 m. The ball's height h (in meters) at time t (in seconds) can be modeled by the quadratic function h( t ) -4.912 + 14t + 2 . — a. Does the ball reach a heighLof 14m? VFrite an equation and use the discriminant to answer. b. How long does it take for the ball to hit the ground? f: .. m -- v $ COOrdS ^ ?? % 1 ' % * i 1 !U i l 1 c. What is the maximum height of the ball can reach? i a ft r^ Module 4 - Quadratic Relations and Systems of Equations i ! 4.1 Circles i For 1- 2 , write the equation for the circle described. 1. C(-3, 2), r = 4 { m} uv- ir - IL 2. C[1, -4], P(-3, 5 ) 9 - ' •• ( -1 - I ) 1 I d f Si iz 1 V v /2 !/ f t .- S " j ’ Hi ) AA ' 6 iw ! 3. Identify the center and radius of the circle with equation (x + 2) 2 U r i ) r= + (y + l) 2 = 36 For 4-5, rewrite the equation of the circle in standard form. Then, identify its center and radius. 4. x 2 + y 2 = — — yl iL Z- VL 2 ^ ( yz -k Cf -l y ) - — 4x -- 24y I- 112 = 0 5. 2x 2 + 2 y 2 - j 16x 4y + 22 y + / 0 S' ~ C VlfY 'C' c l/0 K' J £ x*Kw + C Cro" rf A j >. - /.- ?£i .{ j Ct - H\ { Cy. ~i ) ) ' ' ; 1 £ ’ 4.3 Linear-Quadratic Systems - - For 6 7, solve each linear quadratic system. f 1 iy —— — — = 7 .X y= x 7 = x 2 4x 5 <2 \ V ! X* Z . » &A 1 # ' }0 7 : X‘ : X{ / 20 C5 .--v , r * , I T l: x 2 x 90 y = x + 30 ft 1 " — —— 'l>- hsfi - *C ~ )} y) ^ •JI &. " k / % 4.4 Systems of Three Linear Equations \ i / l^ r f » v • " y w .2 . V - \ r A / K VV<./ vJ • • A \ V For 8-9, solve each system algebraically. 8. — — 20 1 3x + l y + z = 21 2 lx + y + 3c 3x = — 2y + 3? = — 9 9. i x + 2y + 3z : - = 9 1 : =5 x + 4y — z = — 5 x + 3y + 2 z 3 I ! 2 3 i i ! I I Unit 3 - Polynomial Functions, Expressions, and Equations Module 5 - Polynomial Functions 1; W r V ^ 5.1 - Graphing Cubic Functions Given the general equation f ( x ) = a Q ( x — h )J ~*! 4 k , write the specific equation for the graph. , ,3 A p 2. L y . ! i <4 V, i , ;4 1 " i : i (3.5, 2) ! 2 : i —— (3, 1 ) ( 2.5, 0) 4 : -2 i • • !• i • . ! — 0- • 1 i 2/ 1 f £<) (&. W i x h» 4 2-• i I : 4 : ! ; i j 7 For 3-4, tell what transformations have been applied to the graph of / (x ) = x 3 to produce the graph of g ( x). Then, graph g (x) by finding the point of symmetry and at least one point on each side. = (i (x - l) ) 3- g ( x ) 2 W T \ Tj TTil 6 } 4fr j + 3 H- 8 1 1 ' - r " • • - ' 4 11? ' a \ . i~ - p — T : •i . 4_ , 1 J ::n ; r— i | i8 . _ —ig . LXXi - i r i i 6 i 4 ? f 2 0 -4 F . ~ ' T iL x I 2 L4 " " i —b , T r " L , ifTt rn ! 2 J iJ i — — 3(x + 2) 3 — 1 - -I I ! ' 4. g { x ) ! i r~ j J . J -1 1 i > ... l , 5.2- Graphing Polynomial Functions _& ! J _ —\ jj ' 1 „ For 5 -7 , identify whether each function graphed has an odd or even degree and a positive or negative leading coefficient. - 5. 7. 6. i \ f 'FiV * « * - 4 * x * ) 1 r For 8-9, graph each function without a calculator. State the degree, end behavior, x- and y- intercepts, and the intervals where the function is positive or negative. 8. f i x) = -(x - l ) 2 (x + 3) 9 . f ( x ) = x (x + 2) (x - 3 )(x - 1) Degree : x - intercept(s) : X - ? % i Degree: x - intercept(s): I y - intercept: > rJ ' ' l +ry J rr) - OCoil ) oCZ .Gtf Positive:, C O i 2) Positive: . k > ! Negative : O y - intercept: J V Negative : / (rlfO ) (...) / \ 4 8 ( v i fy ty / / • + 2 1 X h-> /, + f — X 4 > 2/ 4 4 8 • i 11 i - For 10 11, graph each function on a graphing calculator to determine the number of turning points, the number of global maximum and / or minimum values, and the number of local maximum and /or minimum values that are not global. 10. f ( pc) = x(x Turning Points: — 4)2 — — 2)(x + 1) x 2 (x Turning Points: Global Maximumfs]: Local = 11. f ( x) Maximumfs]: Global Minimum (s): Global Maximum (s): Global Minimum (sj: Local Minimum (s): Local Maximumfs): Local Minimumfs): Module 6- Polynomials 6.1 - Adding and Subtracting Polynomials For 1-2, perform the indicated operation. Write your answers in standard form . g( x) — (3x 3 — 6x — 4 + 9x ) 2 1. h( x ) + k ( x) 4\ f ; / = ( 2x 2 1 V } } 1 1 \) Li . V v = (llx3 — — x2 2 + 5x) *9 ?X l * 2x + 6) /e (x) y./ >) V * — 2. h (x ) - g ( x ) \\ t A -- \> v J v 1W | A A T i h( x ) 6.2 - Multiplying Polynomials .. - t p ? ' T Vs . .. • :3 'J -V •'7 ' ^ AV • * 1r fc «/ r div * ' A - For 3 4, perform the indicated operation. Write your answers in standard form. l (x ) =x+2 m (x) = y 2 -I- 2 y — 12 / y? v 3. n (x) m(x) n (x) . = 4x 2 ( 4. Z (x) m (x) J i y y n ^ L' / V ' - 6.3 The Binomial Theorem - For 5 6, use the Binomial Theorem to expand each binomial. 5 . (x + y ) 4 X ^ 4- 6. (2 x — y) 3 - For 7 8, find the specific term of each expansion. 7. 3rd term of (x + 3y) 4 7 ra 8. 2 nd : — term of ( 3x + l) 5 i & yri i V A ) r VA C. V’ V N-> . ..V . ...J yi 9 r > l ! ' ** * J 6.4 - Factoring Polynomials 9. Complete each of the polynomial identity: a % . * ** a. Difference of two squares: 7 t f M 4 63 rj (Cx Vlp ) b. Perfect square trinomials: ' $ d. Difference of two cubes: 9 - 'Wr' / L " M J A c. Sum of two cubes: I w %, % I f; "" * T For 10-15, fully Factor. — lOx — 48 10. 2x 2 11. 4x 3 - lOOx rf : £*2 «£# rj tfua" 13.16x 12. x 3 - 64 2-8 15. 3x 2 - 75 x 14 . 3 x - 48 x+1 TxCX -t t ) For 16- 17, factor each polynomial by grouping. I 16.( 5 x 3 fr f / - 6 xz ) - 15 x + 18 ) 17 . pr 3 + 3r )f 21r - 7/ 2 IP; w* K~ \ -J "W is? <• , X - r- O .V t U I r*, rr t 6.5 - Dividing Polynomials For 18- 19, divide using long division. Write the result in divident remiander . 18 . (x2 - x - 6) ^ *H ( 2 1 9. (2x 3 - 10x 2 + X - 5 ) T (X - 5) (x — 3) ''v et ^ 1x -& = ( divisor )( quotient ) + l 2 i Fi Af ’ ft V -- •rwTi; N K. M divide using synthetic division. Write the result in For 2 20 . ( 3x 3 — - 8x + 4x 6) (x — 2) 2 2J 3 -* 21. (x - •r* ' cv ': w?- - "5k x& NT * Wi dividend divisor 4 + 2x = quotient + 3 — remainder divisor “ >> 3x + 1) (x + 3), ^ N x/ 3 y * *** V « o %I I For 22- 23, determine whether the given binomial is a factor of the polynomial p( x ). If it is, find the remaining factors of p(x ) and write p ( x ) in factored form. / 22 . p ( x ) = x 3 + x 2 — lOx + 8; x — 2 t .1 !l • 2 > 23. p ( x ) *** vif ‘ Y — ..v . ^ /1 ^ = x 3 — x 2 — 36x + 18; x 10 I‘ "'•''A? ‘ - >AT " p-- ' S? . Module 7 - Polynomial Equations 7.1 Finding Rational Solutions of Polynomial Equations For 1- 2 , list all possible rational zeros/ roots for the equation. Find the actual zeros/roots of the function and write the function in factored form. L / (x) - x 3 + Sx 2 - 8x - 48 5 - & 41 'L ZY - LI > Cx -3)frV«xW - * i — LJ 1 * (WfffDW ) t u. i 2. p (x) iU = 2x 4 + x 3 — 19x 2 — 9x + 9 Q l -a I i 3 4 3. 4 x 4 - 64x 2 = 0 q 1( iQ o 5. x4 - 14x 2 + 45 = t * r< tfa 9 2 4.(x 3 + 3x| fx ^ ***> ^~ — iS3a sa? • .JV —3 * C f 0 / - -v. * i **«**!.', \T X / if?I s£ ^ W .7 V iVvc ****** ? - ... jy •• " .> IS tr o 6. x4 - 7x 3 - 3x 2 0 6^-5 ) j° ' w. w* : :-i. .ffv .K^- -11 ? For 3-6, solve each polynomial equation. t ( jl - H5 * / ' ~ » V + 63 x - S4 = 'Q Z - s .i Tor 7-8, solve eaCh-eqtfatfofi by factoring. ^ { 7 4x 3 )£ + x 2)(— 4x — l) = 0 xf ) ) WffX+ t) ^ 8. Xs - 2x4 - 24x 3 ^ OcZ- tKfW >=° =0 «HV> **'- a X* £X ~£ )&/+ -- <5 7.2 Finding Complex Solutions of Polynomial Equations \ V For 9- 11, solve each equation by finding all roots. ) +(3x - 6)= 0 ) VX t x+ x - t '2) = ° 9. (x 3 - 2x 2 10 . x 3 + 3x 2 10 \ X,+X+ ) WX+) - o (xM) t r j) - o - “ — 3r' - t Z ( T\ ” (« . r £~ i* m ~i .•v , s r <78r *«r« " ^ - 2: 13. 2 i and V 3 C+ DCX- 4 ) t m ) ) (y 2- r Ar-z*- *< + a fiEMl: i ± X ±- 12.1, 4, and — 3 % ^ II Ti' For 12-13, write the simplest polynomial function with the given roots. -( li^hsmW £xz - t \^i C !OiZ0 — 14x — 20 = 0 23 -g| I 3 - / - 2 £> ^ ll /x 3 - 3x 2 + /4x - 12 )= 0 ' ffo&{ <; -6 ! FS! 2 +*** ' 2.. C*-i\ ) bun ) (x-JflOtij$ ) y = 2 t J u / . l f x Pi / A LA > 11 -v / 4 " > «• 1 \ 1 ' f * I i 1 ' . ,** J Unit 4 - Rational Functions, Expressions and Equations Module 8- Rational Functions 8.1 Graphing Simple Rational Functions For 1-2, identify the asymptotes, domain and range in set notation for each function. ^ l. g(x) = HA 2. g ( x ) = x +S VA Y -- 1 +8 f « v tc 3. Rewrite the function in g ( x ) = a * 1 + k or g ( x ) + k form, then find the asymptotes and domain and range and sketch the graph of g ( x ). v * X -f v, r r 4 Kfcr*> = s*ssa 4x - 5 Six ) = - - 2 5 • X 2. * ^ 14^ I 3 : I . ^ • ! i f -4 -2 # •/ L ! p *: . • : ^: ?» ; I I j 0_ . ; 2 -{ i h X 4 ( " ~4 * l 4. Write the equation of the graph in the format of f i x ) : — — — — —— h— — — : 6)- ^ i • sfifi»' •#&*/*** or f i x ) y ! *i I = a (- * ) + k = i ^ =- Pt - ' ' f ) "%) 8.2 Graphing More Complicated Rational Functions For 5-6, identify all vertical asymptotes, holes, and horizontal or slant asymptote of each rational ~ O' ' 7* ~V function. Then state its domain. / ., . .. 2 3 X X 4 + X l 6. / (x) = 2 2 X ~ 8 ^ 5. f i x ) = 2 " » - -3x + 27 ' - tTvujn W) - *ft t - T! Vertical Asymptotes: Horizontal or Slant Asymptote: Holes: Domain: ... . _ »tr SL .X » 3 xfcH ! * r / X + - Vertical Asymptotes: Horizontal or Slant Asymptote: LX ~ Holes: ( y| * Domain: ^ / i ^ i ! ! 12 i i ! I -2 x+l 7. f { x ) = 8. fix ) Vertical Asymptotes: Horizontal or Slant Asymptote: iA ^ i jAfr Holes: _ " Domain: [ Xtoi Vertical Asymptotes: Horizontal or Slant Asymptote: jQ»n . Holes : Domain: • xl = — x 2 U ** ° * Z. Module 9 - Rational Expressions and Equations r 9.1 Adding and Subtracting Rational Expressions v For 1- 2 , add or subtract. Identify any excluded values. — rt ~ 2K 1WA X +4 -X -12 + X -4 CkW ) 1. X2 &x mx Hj- ifi (Kit CM ) 3.fix - 3 + -+2 (M ) 3 X 18 m X (M> ) ( - ) 3 X 2 ~1 2. X 2 ^ { - - Gt DCMD . n&. L >' ctrocm ) >! s '•S 9.2 Multiplying and Dividing Rational Expressions . ^IE For 3- 4, multiply. Identify any e clpcjed y kies. 7x 3 + 49x 2 —+ 3. X X +7 9 ^ ‘CvX3 / / g For 5 -6, divide. Identify any excluded values. 5. ( ^ - 6 (X 2) “* X - -2 27 x+9 x- io 10(^ 10) - - 3 X 2 QX 3 4 pfioi&is) i f 9.3 Solving Rational Equations Solve each equation algebraically 7, i X- 2 2* 1 i - it•» .i(? < ^ f — £ ‘b( Xr& ~ C -h - ) 4 = y -3X f -42 - $ V xV ' * / I - 7X + 10 3 i t x .X L t e V. X it ! ;!x v' a *"* »** /7 #9 L ij 4 + = + 4) ^ CfH 0 * i x 2 -4 %-2 CXrZ ) ( jit7 ) H -i n X=2 13 \ ; r i I \ \ 10.1 Inverses of Simple Quadratic and Cubic Functions For 1-2, graph the function f [x ) for the domain { x \ x > 0}. Then write and graph its inverse function, x fC. , \x ) . r t 1. f (x) = 0.25x 2 . 2• f * ^ r 4te~ 0 . g .J ——4i—i—6— —8— —10— —12x 2 i i i i i i i i pYv j 4 g 2 ! X. i -7 ‘ - T i ~ 0 x. ml . /(x) = 0.5x3 V i .y j '• i J r> O f7 — 1 . 4 - : 2 \ uc + 2 4 — - 4 i 2 I —101—1—12h- 1 1 8 . X 4. f i x ) = x 3 - 2 i "’r —4 > y :• - r.il- 4 i 2 ' V i 0 2 — -4 ! L ._*l X :i — 4 ’ ) -im f ~& ^ j t -X—rar * ! 1 f 0& - £ ifin i I i ^ X —46 4 4 \ ! * i - f T ”‘ : * ' i 1 For 3 -4, graph the function f [x) . Thep write and graph its inverse function, / (x) 3 / ,r> >• • ^ J 744V .- vm *»: •vvXux 's*.,, U\ - — */o ***#& ?**•-"** ‘ 'C* ! For 5 -6, use the function d(t) = 4.9 t 2 which gives the distance, d, in meters, that an object dropped from a height will fall in t seconds. 5. Write its inverse function t(dj for the time, t, in sec . meters 'L eU 4.11 li .*> f r for an object to fall a distance of d ) r) ‘# 4 AZ . ; / ! 1 6. Find the number of seconds it takes an object to fall 150 meters. Round to the nearest 10th of a second. U5 14 ; 1 10.2 Graphing Square Root Functions For 1-2, find the endpoint and two additional points to graph each function. Identify the domain and range . > —4 1. f { x ) = Vx 10 ft A * f ' 2 “ Z- 2 6 6 -8 8 2 X 8 10 6 6 4 8 10 ** • .4« -1 0 10.3 Graphing Cube Root Functions*' % / 11.2 Simplifying Radical Expressions \ u For 8-13, simplify the expression. Assume that all variables hire positive. All exponents should be .. . , positive in simplified form. Rationalize any irrational denominators . B VOT Q — 11. vss\. ffiz 64 V* • 4_?/v V 2 7 - V F - V9 1 0. % V? Vi3 • 3 % %,3 ^ *3 ^ $ V? J- . I X y / ' 4 2- + \ 11.3 Solving Radical Equations ; ; ! For 14-17, solve each equation. Identify any extraneous roots. 15. 2 + y/ x 14. (4x + 7)7= 3 ' ^5-2 FFH jp: 6 / J\ +l£ 6 h& - A “ IS « ) ' L/c>W _2 * X 3 . " - ^ 2X ~ 2 => 2! if . = —rr - 1^5 oV ofc-ii ^ 1 7. - ^/ 05 xZ Sx / x -2 J(* - Z ) X -2 x - Mx *u\ 01 (x -3)1* -1) - x +i x + z O - x -3 (F - 2 V 2x - 2 = 6 z *+-Z 2 ; ? -3 v , a x M 6 ' x - 1 0* * 1$ O — 2 =-x . x- Z * v* 0 1BSJ *T (f ^ 18 . The trunk length fin inches) of a male elephant can be modeled by Z = 23 Vt + 17, where t is the ' age of the elephant in years. If a male elephant has a trunk length of 80 inches, about what is his age? .' X j r P1f * ryir . .- •vrf " 43 = 25V/T ' 23 ^ (2. 2 7 . !c *x 4( 0 < 16